A new method for computing the stable invariant subspace of a real Hamiltonian matrix or Breaking Van Loans curse
Peter Benner, Volker Mehrmann, Haitao Xu · Qucosa (Saxon State and University Library Dresden) · 1998
A new backward stable, structure preserving method of complexity O(n^3) is presented for computing the stable invariant subspace of a real Hamiltonian matrix and the stabilizing solution of the continuous-time algebraic Riccati equation. The new method is based on the relationship between the invariant subspaces of the Hamiltonian matrix H and the extended matrix /0 H\ and makes use \H 0/ of the symplectic URV-like decomposition that was recently introduced by the authors.